Exact solutions for logistic reaction–diffusion equations in biology

被引：0
作者：
P. Broadbridge
B. H. Bradshaw-Hajek
机构：
[1] La Trobe University,Department of Mathematics and Statistics
[2] University of South Australia,Phenomics and Bioinformatics Research Centre, School of Information Technology and Mathematical Sciences
来源：
Zeitschrift für angewandte Mathematik und Physik | 2016年 / 67卷
关键词：
35K57; 35K55; 92D25; 92D99; Nonclassical symmetries; Reaction–diffusion equations; Fisher equation; Fitzhugh–Nagumo equation; KPP equation; Exact solutions;
D O I：
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学科分类号：
摘要：
Reaction–diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
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